SHIPBUILDING. 98 SHIPBUILDING. If the ship is made to roll, the position of the centre of buoyancy will be displaced, as shown in Fig. 3. We have then a force acting vertically upward at B', and a force working vertically downward at G', producing a couple Fig. 4. tending to turn the ship back to her upright position. Similarly, if the ship pitches, the centre of buoyancy is displaced longitudinally and the couple acts as before. In cither case, if W is the weight of the ship in tons the mo- changes for every change in the position of the centre of buoyancy, but for angles not exceeding 15 degrees the change is slight. The value of the metacentric heiglit usually given in tables is, therefore, that obtained by inclining the ship tlirough a very small angle. The rolling of a ship when forcibly inclined in still water and then allowed to right herself is like that of a pendulum which has been drawn to one side and then permitted to vibrate im- til it comes to rest. Acted upon by the couple (the moment of which in this case is called the moment of staticiil stability) , she rapidly I'eaches the upright position at a constantly varying angular velocity. As soon as this position is reached the couple ceases to act, while her mo- mentum causes the roll to continue; but be- yond the upright position a couple in the oppo- site direction is formed and this {together with friction and wave-making) gradually checks her roll until it ends, whereupon the new couple sets up a roll in the opposite direction Just as a pendulum returns in its vibra- tion. Tlie rolling continues, though the arcs are smaller and smaller each time, until the vessel comes to rest in stable equilibrium in the upright posi- tion. The oscillations of a pendulum in vibrating are performed in equal periods of time, irrespective of their amplitude ; and this is practically true of the ship, though the wave-making due to the high angular velocity of deep rolls and the in- creased friction due to greater area of immersed surface cause some variation. The mean length of time required for a ship to make a conijilete double roll through a moderate angle in smooth w-ater is called the stiU-icntcr period. In rough ment of this couple is equal to W X G'H, or ^^.^^^j. ^-1,;^ pei-iod is modified by the action of the waves, which gives a constantly varying value to the total righting moment. If the waves pass under a ship in such a way as to add to this moment when the ship is rolling toward the vertical and reduce it when she is rolling away from the vertical, a dangerous condition of af- fairs is produced which may result in her cap- sizing. This condition can only exist when the wave period (time between waves) is practically the same as the ship's still-water period; when W. X G"H'. If a vessel rolls and pitches at the same time the centre of buoj-ancy will be displaced both laterally and longitudinally, and the couple will then tend to act in a plane, mak- ing an angle with the keel which is greater than and less than 90 degrees. If a ship is pressed over by a constant force, such as the wind or the action of the rudder, and the surface of the water is smooth, the righting moment is simply that of the couple. But if the surface of the water is broken by waves the shape of the sub- merged body is constantly chang- ing, thereby moving the centre of buoyancy and adding to or sub- tracting from the righting force due to the couple. When a ship is forcibly in- clined in still water the point JI ( Fig. 3 ) , called the transverse metacentre, is the point in which the vertical line through B' cuts the line G'M, which it does exist the course of the ship with refer- is vertical when the ship is upright: and the dis- euce to the waves should be materially changed, tanee G'M is called the transverse metacentric Since the righting moment is the force which height. Similarly in Fig. 4, M' is the longitudinal makes a ship roll, it is evident that if this force metacentre. and G"M' is the longitudinal meta- is powerful the ship will roll quickly and per- Fig. 5. DIAGRAM BHOWING TSE OF "WATER-BALLAST TANKS IN A MERCHANT PTEAMER. The shaded portion indicates ballast tanks. centric height. In vessels of ordinary type G"M' is so large that there is practically no danger of their turning end over end unless they are very small. G'M, however, is often ver- small, and its value must be very carefully considered. Being so much used, it is commonly referred to as the metacentric height. The determination of it is effected by inclining the ship in still water. It haps deeply, neither of which is desirable. To reduce the time of rolling (i.e. the still-water period) the metacentric height may be reduced as much as is consistent with safety, or the weights in the ship may be moved away from the midship plane if practicable, at the same time preserving the same heisht of centre of gravity. To reduce the amplitude of the roll.
